A person’s present age is two fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. What is the present age of his mother?

Let mother’s present age = \(M\), person’s present age = \(P\).
Given:
\(P = \frac{2}{5} M\) ...(1)
After 8 years:
\(P + 8 = \frac{1}{2} (M + 8)\) ...(2)

Substitute \(P\) from (1) into (2):
\[ \frac{2}{5}M + 8 = \frac{1}{2}(M + 8) \] Multiply both sides by 10 to clear denominators:
\[ 4M + 80 = 5M + 40 \] \[ 80 - 40 = 5M - 4M \] \[ 40 = M \]

Answer: The mother’s present age is 40 years